Alexander Isak capped of a masterful performance with a perfect spot kick to claim three points in extra time, but the Toon had to work for it.
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Nottingham Forest took the lead through a delightful Emmanuel Dennis finish from a Sven Botman error, but it was completely against the run of play.
Either side of the opener Newcastle hit the bar, first from a botched Renan Lodi clearance and then a deflected Sean Longstaff strike.
Forest were riding their luck in their relegation battle, but as it turned out luck wasn't enough to stop Isak.
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The £60million record signing was at his very best, volleying in a cross that looked lost in the acrobatic style of his countryman and hero Zlatan Ibrahimovic.
talkSPORT commentator Lucy Ward said: "I talked before the game about him having the perfect profile for a modern striker - he has agility and he's tall.
"The ball was behind him but he's got such long legs he somehow gets his foot right back and curls it like a karate kick.
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"What an absolutely brilliant goal, he did so well, what an absolutely brilliant finish."
That goal came just before the break, and signalled the away side's dominance, but it took another 45 minutes for them to again capitalise.
Elliott Anderson was denied his first Newcastle goal by VAR after some sublime work from Isak was deemed offside, but the Swede wasn't finished.
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Winning a penalty late on from the wandering hand of a distraught Moussa Niakhate, Kieran Trippier took in the mind games from Kaylor Navas on the spot, but then handed the ball to Isak for him to bury.
"Isak is some player," Ward added after the clinic was complete.
The result leaves Newcastle a point behind Tottenham who have still played a game more, while Forest remain two points above the bottom three.